We tried to do this from birth, but we quickly realized that it was way too traumatic for Henry. The process of whipping off his diaper and urgently moving toward the toilet was too frightening, so we promptly stopped.
But recently, we've been trying again, with much greater success. My Montessori teacher explained that at about six weeks, she starts siting her children on a child-sized toilet after every diaper change, as a way to help them associate the toilet with what goes on in their diapers. She also recommends holding them over the toilet during common times, like before a bath, first thing in the morning, and after nursing. Soon enough, you'll start "catching" pees and poops.
We've definitely caught some pee and poop, although the ratio is still very low. It's a work in progress!
And, as a side note, we use the word "toilet" instead of "potty" because we try to use real words as often as possible as we help Henry build his vocabulary.